Calculate Q1, D7 and P58 from the following data and interpret the results. Weight 0-10 10-15 20-25 25-30 30-35 35-40 40-45 45-50 50-60 No, of person 4 8 30 15 13 6 4 4 1

Solution:

Since the classes are unequal so adjustment is to be made before calculating.

 Weight No. of Person (f) c.f. 0-5 2 2 5-10 2 4 10-15 8 12 15-20 15 27 20-25 15 42 25-30 15 57 30-35 13 70 35-40 6 76 40-45 4 80 45-50 4 84 50-55 0.5 84.5 55-60 0.5 85 N = 85

Now,

For Q1:

Q1 = $$\left ( \frac{N}{4} \right )^{th} \enspace item$$

= $$\left ( \frac{85}{4} \right )^{th} \enspace item$$ = 21.25th item

In c.f column, the value just greater than 25.25 is 27. so, class is 15 – 20

Then,

Q1 = $$L + \frac{\frac{N}{4} – c.f.}{f} \times h$$

= $$15 + \frac{21.25 – 12}{15} \times 5$$

= 18.08

For D7:

D7 = $$\left ( 7 \times \frac{N}{10} \right )^{th} \enspace item$$

= $$\left ( 7 \times \frac{85}{10} \right )^{th} \enspace item$$ = 59.5th item

In c.f column, the value just greater than 59.5 is 70. so, class is 30-35

Then,

D7 = $$L + \frac{\frac{7N}{10} – c.f.}{f} \times h$$

= $$30 + \frac{59.5 – 57}{13} \times 5$$

= 30.96

For P58:

P58 = $$\left (\frac{58 N}{100} \right )^{th} \enspace item$$

= $$\left ( 7 \times \frac{58 \times 85}{100} \right )^{th} \enspace item$$ = 49.3th item

In c.f column, the value just greater than 49.3 is 57. so, class is 25-30

Then,

P58 = $$L + \frac{\frac{58N}{100} – c.f.}{f} \times h$$

= $$25 + \frac{49.3 – 43}{15} \times 5$$

= 26.43